EXAMPLE: Bought a watch for $15 and sold it for $18; what per cent did I
make?
.15)3.00
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20
_Ans._ 20%
Here, $15.00 is the base, and ($18 - $15) $3.00, the gain or percentage.
Now, as 1% of 15.00 is .15, it is evident that 3.00 is as many per cent
of 15.00, as .15 is contained times is 3.00, which is 20.
Proof: 20% or 1/5 of $15 = $3.
The percentage and rate given, to find the base.
RULE.--_Divide the percentage by the rate per cent expressed decimally_.
EXAMPLE: Received $6.40, percentage or interest, for money loaned at 4%,
what was the base or principal?
.04)6.40
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_Ans._ $160
If $1 produces .04 (4 cents) in a certain time, $6.40 must be the
percentage of as many dollars as .04 is contained times in $6.40, which
is 160.
Proof: 4% of $160 (160 × .04) = $6.40.
The amount and rate given, to find the base.
RULE.--_Divide the given amount by 1.00 plus the rate per cent_.
EXAMPLE: Bought a horse at a certain price, and sold him for $84, making
12% on cost; what did he cost?
1.12)84.00
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_Ans._ $75
If I made 12% on cost, every dollar invested gained 12 cents; hence, the
horse cost as many dollars as 1.12 is contained times in 84.00, which is
75.
Proof: 12% of $75 (75 × .12) = $9; $75 + $9 = $84.
The proceeds and the rate given, to find the base.
RULE.--_Divide the given proceeds by 1.00 minus the rate per cent_.
EXAMPLE: Sold a wagon for $51, which is 40% less than it cost; what did
it cost?
.60)51.00
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_Ans._ $85
If I lost 40%, or 40 cents on the dollar, I received only 60 cents for
every dollar the wagon cost; hence, it cost as many dollars as .60 is
contained times in 51.00, which is 85.
Proof: 40% of $85 (85 × .40) = $34; $85 - $34 = $51.
NOTE.--The principles of percentage, in one form or another, enter into
nearly all commercial calculations, besides many others. It is therefore
of the utmost importance to business men, clerks, accountants,
bookkeepers, and others, to become expert in percentage, and to adopt
the easiest, simplest and shortest methods in computing interest,
partial payments, trade discount, profit and loss, commission,
insurance, stocks, bonds, taxes, exchange, etc.